Bunuel wrote:

On one exam, the average (arithmetic mean) in a class of 20 students was 80%. A week later, a new student enrolled in the class, and had to make up this exam. If the average on the exam for the class increases to 80.5%, what grade did the new student receive on his exam?

A. 90.5

B. 89

C. 85.5

D. 82

E. 80.5

We are given that the original average for 20 students, on an exam, was 80%. We can use the formula average = sum/number, or equivalently, average x number = sum. Thus, the sum is 80 x 20 = 1600.

We are also given that when a new student enrolls, the average increases to 80.5%. Thus, we can create the following equation in which x = the score of the makeup student:

average = sum/number

80.5 = (1600 + x)/21

1690.5 = 1600 + x

90.5 = x

Answer: A

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